The Marx-type generator, herein simply referred to as a Marx generator, is a voltage multiplying circuit in which N capacitors are charged, with a power source, in parallel, to an input voltage Vch, after which the charged capacitors are switched into a series configuration so that the output voltage, in a temporary short burst, equals the sum of the voltages across each of the capacitors, or N·Vch. This voltage multiplication enables the designer to achieve extremely high output voltages with a relatively low input voltage power supply.
Each Marx generator stage typically incorporates a switch designed to close at a predetermined voltage. At closure, the capacitor stages add, or, in the commonly understood industry terminology, “erect,” to form an overall capacitance that is equal to the individual stage capacitance divided by the number of stages, and the resultant output voltage is the individual stage voltage multiplied by the number of stages.
The simple Marx circuit, schematically depicted in FIG. 1, illustrates a resistively charged circuit, or one in which the stage capacitors, Cs=Cstage (1), are charged via resistive elements, Rch (3). The stage capacitors 1 are additionally connected via switches S (2), so that with nearly simultaneous closure, the stage capacitors 1 are connected in a series configuration. Thus a single stage may be defined by the stage capacitor 1, two charging resistors 3, and a switch 2. For charge voltages from 10's of kilovolts (kV), spark gap switches are employed.
In general, a Marx generator's characteristic impedance is proportional to the circuit's geometrical inductance divided by its series capacitance, calculated under the condition that the stage switches are closed, as follows:
                              Z          source                ∝                                            L              C                                .                                    (        1        )            The generator's capacitance is defined by the simple series relationshipCmarx=Cstage/N,  (2)where N defines the number of Marx stages in the circuit. The generator's inductance is defined as the total of the inductance values geometrically defined for each Marx stage:Lmarx=N Lstage.  (3)From equation (1),
                                          Z            marx                    ∝                                                    L                marx                                            C                marx                                                    =                                                            N                ⁢                                                                  ⁢                                  L                  marx                                                                              C                  marx                                /                N                                              =                      N            ⁢                                                                                L                    marx                                                        C                    marx                                                              .                                                          (        4        )            The voltage realized on the load becomes
                              V          load                =                  N          ⁢                                          ⁢                      V            ch                    ⁢                                                    Z                load                                                              Z                  load                                +                                  Z                  marx                                                      .                                              (        5        )            As a result of equations (4) and (5), large values for Zmarx reduce the voltage efficiency on the load, as the load voltage is highly dependent on the number of stages with respect to the stage capacitance.
Compact applications designed around single capacitor geometries and requiring a large number of stages can result in large source impedances to the extent of a Marx circuit being inappropriate due to voltage inefficiencies caused by impedance mismatches between the Marx circuit and the load. As a result, the primary application of the Marx circuit has been as a trigger source in which high impedance loads are well matched with the Marx generator. See for example Grothaus (U.S. Pat. No. 5,311,067).
Marx generator applications calling for moderate to high energy stores but having non-stringent volumetric constraints minimize impedance problems by employing large stage capacitors. However, for very low impedances, e.g. less than 30 Ohms, driving low characteristic impedances with a typical Marx generator is difficult, if not impossible. As a result, the Marx generator is typically relegated to the role of a voltage multiplier designed to pulse charge an intermediate energy store the coupling efficiency to low impedance loads of which is better than that of the Marx generator itself
To summarize the impedance problem facing designers of a Marx circuit, compact geometries are traditionally best suited for trigger applications characterized by high impedance loads. Applications allowing larger volumes with minor emphasis on energy efficiency can rely on large stage capacitances to better match low impedance loads.
Goerz (U.S. Pat. No. 6,060,791) describes a compact Marx generator circuit that realizes a high energy density geometry via novel packaging designed to reduce the overall circuit length. Ultimately the Marx circuit's inductance was reduced; however, the overall characteristic impedance of the generator was not reduced due to the centrally-located stage switch and the absence of a suitable ground plane. The Goerz geometry therefore produces a low load voltage efficiency.
The basis for higher voltage efficiencies in Marx circuits partly lies in the proper design of stray components, which is obtained by encapsulating the Marx circuit with a ground plane. Proper design of the stray elements leads to a Marx circuit design referred to as wave erection (see D. Platts, GigaWatt Marx Bank Pulsers, Ultra-Wideband Radar: Proceedings of the First Los Alamos Symposium, Ed. BruceNoel, CRC Press, 1991). Suchadesign is also referred to as wave triggering (see C. E. Baum, “Traveling-Wave Switches and Marx Generators,” Switching Note 33, Air Force Research Laboratory/DEHP, Kirtland AFB NM, March 2005), which is essentially the manner in which the stage switches close sequentially in a cascaded manner.
The full Marx circuit is shown in FIG. 2. The classic circuit is well understood. Less appreciated are the stray elements defined by the geometry of the circuit. Stray elements may be considered as stage-to-stage capacitance, and includes the switch capacitance Cswitch (4), the stage-to-ground capacitance Cstray (5), and the stage series inductance Lstray (6). Each of these stray components drastically affects the performance of a Marx generator.
Consideration of the relationships among capacitive elements is critical in the design of a pulse generator. In general, once the voltage across the first switch has collapsed, that potential should be realized across the second gap, instead of being distributed among all subsequent gaps. Furthermore, that same potential should ideally be maximized on the spark gap switch instead of across the associated stray capacitance to ground. As illustrated in FIG. 3a, the voltage on Cstage (7) is distributed across the capacitor divider of the gap switch capacitance Cswitch (4) and the stray-to-ground capacitance Cstray (5). For the potential to be maximized across the switch, Cstray (5) must be much larger than Cswitch (4), and to minimize the amount of energy lost in the stray components, Cstage (7) must be the dominant capacitive element over the stray capacitance. Thus wave erection is made possible by the following condition:Cstage>>Cstray>>Cswitch  (6)
As discussed by Baum, inductance plays a very important role in Marx circuit operation. Large gap inductance, mostly due to suboptimal placement of the switches with respect to the ground plane, leads to slowed switch closure, which in turn increases the temporal jitter of each switch, and consequently the Marx generator as a whole.
Traditional roles for the Marx generator have been complimentary to single shot applications or events requiring repetition rates of up to a few Hz. In such applications resistors are well suited for the charging elements. However, for higher repetition rates and resultant higher charge rates, resistors must be replaced by inductors.
Recovery of the spark gap switches can be problematic when operating at high repetition rates, since the gaseous medium in the gap must de-ionize before the gap can be recharged to a high voltage. For moderate repetition rates, the insulating gas can be physically moved, so as to purge the ionized particulate from the gap. This usually requires bulky mechanical equipment capable of transferring gas at high rates through the entire Marx structure.
An alternative method was described by Moran (U.S. Pat. No. 4,912,369), Grothaus (U.S. Pat. No. 5,311,067), and McPhee (U.S. Pat. No. 5,798,579), in which high pressure hydrogen was used as the insulating medium in the spark gaps. Moran, Orothaus, and McPhee claim short burst repetition rates as high as 10 kHz, but do not discuss the pressurized hydrogen gas flow necessary for such performance.